Centripetal Acceleration and Circular Motion

Circular Motion B C A v Use this to motivate circular motion involves acceleration. Answer: B A ball is going around in a circle attached to a string. If the string breaks at the instant shown, which path will the ball follow? 10

Acceleration in Uniform Circular Motion v2 v1 R R centripetal acceleration Acceleration is due to change in direction, not speed. Since turns “toward” center, must be a force toward center. 12

Acceleration in Uniform Circular Motion Draw in forces. v1 12

Common Incorrect Forces Acceleration: SF = ma Force of Motion (Inertia not a force) Centrifugal Force (wrong object!) Centripetal Force (tension, gravity, friction, normal)

Example: ball in vertical circle A ball of mass 2kg is being swung in a vertical circle with a speed of 10m/s. What is the tension in the rope at the top of the circle? Draw in forces. v1=10m/s g 12

Example: ball in vertical circle A ball of mass 2kg is being swung in a vertical circle with a speed of 10m/s. What is the tension in the rope at the bottom of the circle? Draw in forces. g v1=10m/s 12

Example Suppose you are driving through a valley whose bottom has a circular shape. If your mass is m, what is the magnitude of the normal force FN exerted on you by the car seat as you drive past the bottom of the hill A. FN < mg B. FN = mg C. FN > mg v mg FN R a=v2/R correct 20

Example: roller coaster What is the minimum speed you must have at the top of a 20 meter roller coaster loop, to keep the wheels on the track. Y Direction: F = ma Let N = 0, just touching N mg 25

Summary of Concepts Uniform Circular Motion Speed is constant Direction is changing Acceleration toward center a = v2 / r Newton’s Second Law F = ma 50